Peter wrote:

What would happen if the original was not on board, and there was an
incident?

As far as a pilot's certificate is concerned, if you don't have that handy and
get caught flying an aircraft, the FAA would issue a violation.

IME the first thing the insurance company checks is that all paperwork
is in order. So, if e.g. the pilot was not licensed to do the flight,
the insurer will walk away from it right away.

This is not true. If the aircraft was actually unairworthy (eg. expired annual),
then the insurer would walk away. If the pilot did not have a pilot's
certificate at all, or was not rated for that category and class of aircraft,
then the insurer would walk away. If you have all the paperwork but don't happen
to have it in the plane, you're still insured.

Read your policy. It will tell you what they cover and what they don't.

George Patterson
We don't stop playing because we grow old. We grow old because we stop
playing.